Question

How do you solve \[\dfrac{1}{4}(x + 2) = \dfrac{5}{6}\]?

Answer 1

Hint: First we have to figure out what we have to do. According to the question, this is an algebraic equation and it is asking us to solve the equation. This means that we have to solve and find the value of \[x\]. This can be easily done by cross multiplication of both the denominators.

Complete step by step solution:
The given equation is:
\[\dfrac{1}{4}(x + 2) = \dfrac{5}{6}\]
As we can see that \[\dfrac{1}{4}\]is multiplied with \[x + 2\], so we can also write the equation as:
\[ \Rightarrow \dfrac{1}{4} \times (x + 2) = \dfrac{5}{6}\]
Now, we will simplify this equation, and we get:
\[ \Rightarrow \dfrac{{x + 2}}{4} = \dfrac{5}{6}\]
Now, we will try to solve this equation. We will solve this by cross multiplication method. We will multiply the denominators with the expressions of the either side, and we get:
\[ \Rightarrow 6(x + 2) = 5 \times 4\]
Now, we will solve this, and we get:
\[ \Rightarrow 6x + 12 = 20\]
Now, we will try to make \[x\] alone. So, we will try to cancel \[12\] from the left side of the equation. So, we will subtract \[12\] from both the sides of the equation, and we get:
\[ \Rightarrow 6x + 12 - 12 = 20 - 12\]
Now, we can see that \[12\] is getting cancelled from the equation, and we get:
\[ \Rightarrow 6x = 8\]
Now, to make \[x\] alone, we will shift \[6\] to the other side of the equation. The number \[6\] gets divided by \[8\] when it moves to the other side of the equation, and we get:
\[ \Rightarrow x = \dfrac{8}{6}\]
Now, we can split both the numerator and the denominator in their respective factors, and we get:
\[ \Rightarrow x = \dfrac{{2 \times 2 \times 2}}{{2 \times 3}}\]
Now, we can see that the similar terms can easily get cancelled, and we get:
\[ \Rightarrow x = \dfrac{{2 \times 2}}{3}\]
This can also be written as:
\[ \Rightarrow x = \dfrac{4}{3}\]
This is an improper fraction. When we convert it into a mixed fraction, we get:
\[ \Rightarrow x = 1\dfrac{1}{3}\]

Therefore, the result is \[x = 1\dfrac{1}{3}\].

Note: In Mathematics, we do cross multiplication by multiplying the numerator of the first fraction with the denominator of the second fraction and by multiplying the numerator of the second fraction with the denominator of the first fraction.